BFS_Shortest Path Algorithm

#include <iostream>
#include <list>
#include <queue>
int INT_MAX=1000000000;
using namespace std;

// This class represents a directed graph using
// adjacency list representation
class Graph
{
    int V; // No. of vertices

    //array of vectors

public:
    vector<int> adj;

    Graph(int V); // Constructor

    // function to add an edge to graph
    void addEdge(vector<int> adj[], int v, int w);

    // prints BFS traversal from a given source s
    bool BFS(vector<int> adj[], int s, int d, int p[], int dist[]);

    //to find the shortest path from single source in a graph
    void SPU(vector<int> adj[], int source, int destination);
};

Graph::Graph(int V)
{
    this->V = V;
}

void Graph::addEdge(vector<int> adj[], int v, int w)
{
    adj[v].push_back(w);
    adj[w].push_back(v);
}

bool Graph::BFS(vector<int> adj[], int source, int destination, int prv[], int dist[])
{
    // Mark all the vertices as not visited
    bool visited[V];
    for (int i = 0; i < V; i++)
        visited[i] = false;

    // Create a queue for BFS
    list<int> q;

    //declaring all the values of prev array as -1 since 0 is already present as a graph vertex;
    //declaring all the values of dist array as maximum;
    for (int i = 0; i < V; i++)
    {
        dist[i] = INT_MAX;
        prv[i] = -1;
    }

    visited[source] = true;
    dist[source] = 0;
    q.push_back(source);
    //iterate till the queue is empty
    while (!q.empty())
    {

        //top element of the queue
        int currentv = q.front();
        q.pop_front();
        for (int i = 0; i < adj[currentv].size(); i++)
        {
            //checking if the adjacent node is visited or not
            if (visited[adj[currentv][i]] == false)
            {
                //visiting its adjacent nodes
                visited[adj[currentv][i]] = true;
                //since the next node's previous will be the current node
                prv[adj[currentv][i]] = currentv;
                dist[adj[currentv][i]] = dist[currentv] + 1;

                //pushing the neighbours of current vertex int the queue for
                //further BFS process
                q.push_back(adj[currentv][i]);

                //we'll stop this process when the reach
                //our final destination point in the graph
                //since after finding the destination there
                //is not further use of doing this process

                if (adj[currentv][i] == destination)
                {
                    //once we exit the dist of dest remains max
                    return true;
                }
            }
        }
    }

    return false;
}

void Graph::SPU(vector<int> adj[], int source, int destination)
{
    int dist[V];
    int prev[V];

    if (BFS(adj, source, destination, prev, dist) == false)
    {
        cout << "cant reach that point!";
    }

    else
    {
        //a list to keep track of the path
        list<int> sp;
        int x = destination;
        sp.push_back(x);
        while (prev[x] != -1)
        {
            sp.push_back(prev[x]);
            //assigning the previous node to the path
            x = prev[x];
        }

        //to print the path in the right direction hence reverse the direction;
        sp.reverse();
        cout << "the shortest path from " << source << " to " << destination << " is:: ";
        for (auto it = sp.begin(); it != sp.end(); it++)
        {
            cout << *it << " ";
        }
    }
}
int main()
{

    vector<int> adj[10];
    Graph g(10);
    g.addEdge(adj, 0, 1);
    g.addEdge(adj, 0, 2);
    g.addEdge(adj, 2, 3);
    g.addEdge(adj, 3, 1);
    g.addEdge(adj, 4, 5);
    g.addEdge(adj, 4, 6);
    g.addEdge(adj, 4, 8);
    g.addEdge(adj, 5, 6);
    g.addEdge(adj, 5, 7);
    g.addEdge(adj, 7, 8);
    g.addEdge(adj, 7, 9);
    g.addEdge(adj, 8, 9);
    g.SPU(adj, 4, 9);
    return 0;
}